Question

8(x^2+1/x^2)-(x+1/x)=504

Answer 1

8(x² + 1/x²) + (x + 1/x) = 504
⇒ 8[ (x + 1/x)² - 2] + (x + 1/x) = 504
⇒ 8(x + 1/x)² - 16 + (x + 1/x) = 504
Let (x + 1/x) = P

Then, 8P² + P - 520 = 0
⇒ 8P² - 64P + 65P - 520 = 0
⇒8P(P - 8) + 65P(P - 8) = 0
⇒(8P + 65)(P - 8) = 0
⇒P = 8 , -65/8

Hence, x + 1/x = 8
x² - 8x + 1 = 0 , this is complex quadratic .
So, x ≠ real number
Now, x + 1/x = -65/8
⇒ 8x² + 8 = -65x
⇒ 8x² + 65x + 8 = 0
⇒ 8x² + 64x + x + 8 = 0
⇒ x = -8 , -1/8